A dead-band section is defined with respect to its transfer characteristics in that in the case of input quantities whose magnitude is below a certain preset threshold value it does not supply an output signal whereas it reproduces the input-signal components which exceed the threshold values unchanged so far as their frequency and phase are concerned, though with the amplitude reduced by the constant magnitude of the threshold value.
In addition to dead-band sections of the above type, there are a number of control-loop components with a high degree of nonlinearity which serve for the execution of switching functions, for example, hysteresis elements, relay or three-point elements, which may likewise incorporate preset response thresholds, with the latter, however, serving primarily to secure unambiguous circuit states. The introduction of an artificial dead band into a control loop has a beneficial effect on corrective energy consumption only because the final control elements are not actuated so long as the deviations are below the response threshold of the dead-band section. Only when external disturbances or dynamic events in the control loop give rise to deviations which result in an overshooting of the response thresholds of the dead-band section are forces and/or moments generated which tend to reduce the deviation, but only until the response thresholds are again undershot. Especially during periods and operating conditions when external disturbances affecting the controlled system are slight, the system will remain within the range of the dead band for a relatively long time and consume no corrective energy.
Now from these basic facts it follows directly that the absolute value of the response threshold is a direct measure of the attainable accuracy of the control system, and that the demands for saving corrective energy and for accuracy conflict with each other. While the accuracy increases when the range of the dead band is increased, the frequency of corrective interventions also increases, and with it the consumption of energy. If, on the other hand, the deadband is dispensed with altogether, the final control elements will be actuated even by the unavoidable system and measured-value noise, and an increase in accuracy will be limited by the increasing stochastic excitation of the control-loop dynamics. Moreover, the noise level in a control system, that is, signal noise and system dynamics, is dependent, apart from external disturbances, in large measure on environmental and operating conditions, such as temperature fluctuations, parameter tolerances, aging processes and the like, which results in a sizable range of variation and considerable uncertainty in the system behavior of conventional control loops and does not permit the setting up of a fixed dead band that is optimally adjusted to changing operating conditions. Thus, once a dead band has been set to a fixed value allowing in particular for the high-frequency noise level for nominal conditions, the "effective dead band", that is, the actually effective deadband range remaining between noise amplitudes and threshold value, changes in an inverse ratio to the magnitude of the disturbing noise, and the behavior of the control loop with respect to accuracy and corrective energy required changes with it. On the other hand, the effective component of an artificial dead band of non-negligible size represents in control loops in every case a substantially nonlinear, and more particularly a discontinuous, transfer element which under certain operating conditions results in limit-cycle vibrations. In linear systems, that is, in control loops whose components --the controlled system, sensors and final control elements--can be described with sufficiently good approximation through linear or linearized transfer elements, pains are therefore taken to avoid the introduction of artificial dead bands. In such cases, the influence of the measured-value noise is usually suppressed so far as possible by means of linear low-pass filters, which, however, has an adverse effect on system stability since low-pass filters inevitably result in phase losses.
Limit-cycle vibrations should generally be regarded as particularly critical when they occur in control loops whose controlled systems include components capable of vibrating, especially elastic structural elements. This is the case particularly with air- and spacecraft, because of their light, weight-saving construction and/or large physical size.
Because of the extremely low self-damping of such structural vibrations, control systems for elastic vehicles of this type tend to be excited to limit-cycle vibrations whose frequencies coincide with the structural resonance frequencies, which may result in dangerous vibration excitation, excessively high mechanical structure loading, and ultimately the destruction of the vehicles.
Moreover, intermittently operating final control elements such as stepper motors or pulsed jet nozzles are frequently employed to produce the forces and/or moments required for stabilization, and their sudden intervention in the system promotes resonance excitations over a broad spectrum of frequencies. In the case of attitude control systems for vehicles of this type, so-called modal controllers have therefore been proposed, that is, the controller networks or algorithms commonly employed in the past for the simultaneous damping of every mode of natural vibration are expanded to include a second-order observer and an associated state controller. Aside from the high complexity, which increases with the number of modes of vibration to be allowed for, and from the cost of realization of the controller, such concepts in practice are rendered largely ineffective by unavoidable mismatching of the observers due to uncertainty and range of variation of the modal parameters.
To prevent the excitation of structural resonances in another case, the hysteresis range of the hysteresis element of a pulse-duration/pulse-frequency modulator employed for the pulsing of jet nozzles was adaptively modified in such a way that the repetition rate of the corrective interventions does not coincide with a structural resonance frequency. With this technique, the intervention in a highly nonlinear element of the modulator circuit, namely, its hysteresis element, simultaneously alters the amplitude and phase ratios in a manner that is difficult for a control engineer to follow and can only be determined approximately by complicated analytical methods.